Zagreb-Based Indices of Prime Coprime Graph for Integers Modulo Power of Primes

The prime coprime graph is a graph in which every pair of vertices is adjacent if and only if the greatest common divisor of the order of both vertices is equal to one or relatively prime. This study aims to analyze the general formula of the first and second Zagreb, and hyper Zagreb indices of prime coprime graphs for a group of integers modulo power of primes. The correlation between these indices is found to have a strong significant correlation; in other words, if one index increases, then the other indices also increase with a coefficient correlation greater than 0.95. We also demonstrate this correlation in one equation and our results improve the understanding of Zagreb-based indices.